Answer:
a) 4 m
b) 24 m/s
c) 0.174 kg
Explanation:
a) Tension in string equation
The information given are;
The wavelength is equal to the rope length , λ = L
The tension = 100 N
The displacement of a point on the rope is y(x, t) = (0.1 m) sinπ x sin 12πt
Given that the wavelength = the length of the rope, the rope is on second harmonic
L = 2·n and the length of the wire = 2 × 2 = 4 m given the dimensions are in meters
b) Where k = 2·π/λ
v = ω/k = 12π/(2·π/λ)= (12π/2π)×λ = 24 m/s
c) f = v/λ = 24/4 = 6 Hz
[tex]f = \dfrac{\sqrt{\dfrac{T}{m/L} } }{2L} = \dfrac{\sqrt{\dfrac{100}{m/4} } }{2 \times 4}[/tex]
[tex]6 \times 8= {\sqrt{\dfrac{100}{m/4} } }[/tex]
m/4 = 100/2304
m = 0.174 kg.
How much does the speed of a car increase if it accelerates
uniformly at 2.5 meters per second squared for 5 seconds?
Answer:
12.5 m/s
Explanation:
a = Δv / Δt
2.5 m/s² = Δv / 5 s
Δv = 12.5 m/s
i) A 100 W and 60 W bulb are joined in series and connected to the mains. Which bulb will glow brighter? Why? ii) A 100 W and a 60 W bulb are joined in parallel to the mains. Which bulb will glow brighter? Why?
Answer:
i) 60 W
ii) 100 W
Explanation:
In each case, the bulb that dissipates the most power is the bulb that glows brighter. Power is voltage times current (P = VI). Using Ohm's law, we can rewrite this as P = I²R or P = V²/R.
Bulbs are rated at a certain power for a certain voltage. P = V²/R, so the bulb with the lower resistance will have the higher power rating. Therefore, the 100 W bulb has a lower resistance than the 60 W bulb.
i) They are in series, so they have the same current. P = I²R, so the bulb with the higher resistance will glow brighter. That's the 60 W bulb.
ii) They are in parallel, so they have the same voltage. P = V²/R, so the bulb with the lower resistance will glow brighter. That's the 100 W bulb.
64. A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance
Answer:
=33 .3×10^6Ω
=33.3M Ω
Explanation:
We were told to calculate the Resistance value,
Given the heart pacemaker fires as 72 times a minute, which is the time constant
Then we can convert the pacemaker fires of 72 times a minute to seconds for unit consistency.
1 minutes= 60secs
Then ,Time constant τ=60secs/72=0.8333 seconds
Time constant τ can be calculated using the formula below
τ= RC
Where R= resistance
C = capacitance
Then making RESISTANCE subject of formula we have
R=τ/C
But Capacitance=25.0-nF = 25×10^25F
Substitute the values we have
R=0.833/25×10^25
=33 .3×10^6 Ω
But can still be converted to M Ω= 33.3M Ω
Therefore, the resistance is 33 .3×10^6 Ω or 33.3M Ω
NOTE: 1M= 10^6
The value of the resistance will be "3.33×10⁷ Ω".
Resistance based problem:According to the question,
Capacitor, C = 25.0 nF
60 sec - 72 fires
now,
Time for 1 fire,
[tex]t = \frac{60}{72}[/tex]
[tex]= \frac{5}{6} \ sec[/tex]
Now,
⇒ [tex]V = V_0 (1-e^{-\frac{t}{RC} })[/tex]
[tex]0.632 V_0=V_0(1-e^{\frac{-\frac{5}{6} }{R.25 n C} })[/tex]
[tex]e^{-\frac{1}{R\times 30\times 10^{-9}} } = 1-0.632 = 0.368[/tex]
[tex]= 2.72[/tex]
By taking "log" both sides,
⇒ [tex]ln \ e^{\frac{1}{R\times 30\times 10^{-9}} } = ln \ 2.72[/tex]
hence,
The Resistance be:
⇒ [tex]R = \frac{10^9}{30}[/tex]
[tex]= 3.33\times 10^7 \ \Omega[/tex]
Thus the above approach is right.
Find out more information about resistance here:
https://brainly.com/question/76343
The same motor is used in rockets with different masses. The rockets have different accelerations. According to Newton’s second law, how is acceleration expected to change as the rocket mass increases? As rocket mass increases, acceleration decreases. There are no changes in acceleration, as it would depend on the amount of force. As rocket mass increases, acceleration increases. Acceleration cannot be predicted based on changes in mass.
Answer:
As rocket mass increases, acceleration decreases.
Explanation:
From Newton's second law of motion;
F= ma
Where;
m= mass of the object
a= acceleration of the object
Hence we can write;
a= F/m
This implies that an increase in mass (m) will lead to a decrease in acceleration if the force on the object is held constant.
Hence, if the rockets have different masses, they will have different accelerations.
Hello!
---------
As rocket mass increases, acceleration decreases.
Hope this helps! The rest are available on Quizlet at "Unit 6: Lesson 4 Force, Mass and Acceleration". Thanks and good luck!
Which units represent density? Select all that apply.
Answer:
D=M/V. That's the formula. Density is expressed, in cubic centimeters.
Explanation:
Answer:g/m³
g/cm³
-kg/L
-kg/cm³
Density in physics, is defined as the mass of the object over its volume. Density is considered as how much matter is contained in a single object by its volume or the matter that it occupies.
D = m / v
Explanation:
just want to double-check that you understand a practical consequence of the expansion of the universe. Light reaches us from a very distant galaxy. The time the light took to cross this distance and reach us is 10 billion years. The distance this light has crossed in this time is probably
Answer:
The distance of the light is 9.4608 x 10^25 m
Explanation:
Time taken by the light = 10 billion years = 10 x 10^9 years
speed of light = 3 x 10^8 m/s
speed of light in m/years is = (3 x 10^8)/(60 x 60 x 24 x 365) = 9.4608 x 10^15 m/year
distance = speed x time
therefore, the distance of this light = 10 x 10^9 x 9.461 x 10^15 = 9.4608 x 10^25 m
Answer:
more than 10 billion light years due to expansion of space
Explanation:
How do parts of a fancy cup (metal like cup) work together to keep a drink cold?
Answer:
“They may feel colder but that's only an illusion,” Dr. Begley says. “Copper mugs actually absorb heat from the room faster than a glass.” Copper is an excellent thermal conductor, meaning it transfers heat from hot sources (like the room or your hand) to cold sources (like your drink) very efficiently.
Explanation:
A ball is thrown upward from an initial height of 1.5m the ball reaches a height of 5m then falls to the ground . What Is the distance traveled by the ball?
Answer:
The distance traveled by the ball is 8.5 m
Explanation:
Initial height of the ball, h₁ = 1.5 m above the ground
final height of the ball, h₂ = 5m
Upward distance = distance traveled by the ball from a height of 1.5m to 5m = 5m - 1.5m = 3.5 m
Downward distance = distance traveled by the ball from 5m height to the ground =5m - 0 = 5m
Total distance traveled = upward distance + downward distance
Total distance traveled = 3.5 m + 5m = 8.5 m
Therefore, the distance traveled by the ball is 8.5 m
If a suitcase has a mass of 20 kg, what is the force of gravity acting on it?
Explanation:
Assuming the suitcase is near the surface of the earth, g = 9.8 m/s².
F = ma
F = (20 kg) (9.8 m/s²)
F = 196 N
A student uses a spring scale attached to a textbook to compare the static and kinetic friction between the textbook and the top of a lab table. If the scale measures 1,580 g while the student is pulling the sliding book along the table, which reading on the scale could have been possible at the moment the student overcame the static friction?
Answer:1860g
Explanation:The force would have to be greater than 1580g, which is when the student is pulling the sliding book with the spring scale
A 310 turn solenoid with a length of 18.0 cm and a radius of 1.60 cm carries a current of 1.90 A. A second coil of four turns is wrapped tightly around this solenoid, so it can be considered to have the same radius as the solenoid. The current in the 310 turn solenoid increases steadily to 5.00 A in 0.900 s.(a) Use Ampere's law to calculate the initial magnetic field in the middle of the 310 turn solenoid.T(b) Calculate the magnetic field of the 310 turn solenoid after 0.900 s.T(c) Calculate the area of the 4-turn coil.m2(d) Calculate the change in the magnetic flux through the 4-turn coil during the same period.Wb(e) Calculate the average induced emf in the 4-turn coil.VIs it equal to the instantaneous induced emf? Explain.(f) Why could contributions to the magnetic field by the current in the 4-turn coil be neglected in this calculation?
Answer:
Given that;
Number of turns in the solenoid N = 310
Length of the solenoid L = 18 cm = 0.18 m
Radius of the solenoid r = 1.60 cm = 0.016 m
Current in the first Circuit I₁ = 1.90A
Number of turns in second coil N₂ = 4
Final Current solenoid I₂ = 5.0 A
Time interval to change the time Δt = 0.9 s
a)
According to Ampere's law, magnetic field inside a conductor is calculated as;
B₁ = ц₀N₁I₁ / L
(ц₀ = 4π × 10⁻⁷ constant)
therefore we substitute
{(4π × 10⁻⁷) × 310 × 1.9A} / 0.18m
= 0.0041 T
b)
Magnetic field inside the solenoid after t = 0.9
B₁ = ц₀N₁I₂ / L
= {(4π × 10⁻⁷) × 310 × 5.0A} / 0.18m
= 0.0108 T
c)
Area of coil is
A = πr²
A = π × ( 0.016 )²
A = 0.000804 m²
d)
Change in magnetic influx is
dФ = (B₂ - B₁) A
= ( 0.0108 T - 0.0041 T) × 0.000804 m²
= 0.0000053868 ≈ 5.39 × 10⁻⁶
e)
Average induced emf is
e = -N₂ ( dФ / dt )
e = ( -4 ) ( 5.39 × 10⁻⁶ / 0.9)
e = - 2.39 × 10⁻⁵V ( NOTE, this is not equal to the instantaneous induced emf )
f)
The induced emf is very low, so the contributions to the magnetic field in the coil is Negative.
A net force of 0.7 N is applied on a body. What happens to the acceleration of the body in a second trial if half of the net force is applied?(1 point) The acceleration is double its original value. The acceleration is half of its original value. The acceleration is the square of its original value. The acceleration remains the same.
Answer:
The answer is The acceleration is double its original value.
Explanation:
It is because of the second trial of accelaration. Because of this, an object's acceleration doubles from its original value.Hope this helps....
Have a nice day!!!!
Answer:
The acceleration is half of its original value
Explanation:
PLEASE ASAP! I SENT A PHOTO CHECK AND TELL!
Answer:
Answer B is the correct answer: "Motion of one projectile as seen from the other is a straight line."
Explanation:
Let's write the equations of motion for each projectile, using that projectile [tex]a[/tex] is launched with velocity [tex]a[/tex] which has components associated with the angle of launching, given in x and y coordinates as: [tex]a_x\,\,and\,\,a_y[/tex].
Similarly, assume that projectile b is launched with velocity [tex]b[/tex] with components due to the launching angle = [tex]b_x\,\,and \,\,b_y[/tex]
then the equations of motion for the two projectiles launched at the same time (t) from the same spot (position that we assume to be at the origin of coordinates to simplify formulas) are:
[tex]x_a=a_x\,t\\y_a= a_y\,t-\frac{1}{2} g\,t^2\\and\\x_b=b_x\,t\\y_b= b_y\,t-\frac{1}{2} g\,t^2[/tex]
therefore, from the frame of reference of projectile "b", the x and y position of projectile "[tex]a[/tex]" would be:
[tex]x_{a\,b}= x_a-x_b= a_x\,t-b_x\,t=(a_x-b_x)\,t[/tex] which is linear in "t"
[tex]y_{a\,\,b}=y_a-y_b= a_y\,t-\frac{1}{2} g\,t^2-\left[ b_y\,t-\frac{1}{2} g\,t^2\right]=(a_y-b_y)\,t[/tex] which is also linear in t.
Therefore the motion of one projectile with reference to the other is a straight line (answer B)
Notice as well that this two projectiles cannot collide because they have been launched together, and supposedly at different speeds and angles. The only way that they can share the same x-coordinate and the same y-coordinate at the same time "t" is if their velocity components are equal, which is not what we are told.
[tex]x_a=x_b\\a_x\,t= b_x\,t\\and\\y_a= y_b\\a_y\,t-\frac{1}{2} g\,t^2= b_y\,t-\frac{1}{2} g\,t^2\\a_y\,t=b_y\,t\\a_y=b_y[/tex]
the resistance per meter is 10 ohm. if the resistance of the material of the wire is 50 then 10^-8 ohm. find the area of cross section of the wire.
the question is at some point wrong or missing a word please help me with the question and answer!
Answer:
5×10⁻⁸ m²
Explanation:
I assume you mean the resistivity of the material is 50×10⁻⁸ Ωm.
R = ρL/A
10 Ω = (50×10⁻⁸ Ωm) (1 m) / A
A = 5×10⁻⁸ m²
The cartesian coordinates of a point in the xy plane are x = −7.11 m, y = −4.41 m. Find the distance r from the point to the origin. Answer in units of m.
Explanation:
Use Pythagorean theorem:
r² = x² + y²
r² = (-7.11 m)² + (-4.41 m)²
r = 8.37 m
Use trig to find the angle.
tan θ = y / x
tan θ = (-4.41 m) / (-7.11 m)
θ = 31.8° or 211.8°
Since x is negative and y is negative, the point is in the third quadrant, so θ = 211.8°.
Or, if we subtract 360°, θ = -148.2°.
The image formed is 0.25 times the size of the object and 10 cm behind the pinhole. If the height of image on screen is 6 cm what is the distance of the object from the screen?
Answer:
40 cm
Explanation:
Magnification of a pinhole camera is given by;
M= height of image/ height of object
Since;
M= 0.25
Height of image = 6cm
Height of object = height of image / M
Height of object = 6/0.25 = 24 cm
Height of image/ height of object = distance of image from pinhole/ distance of object from pinhole
Since the distance of image from pinhole = 10cm
Let the distance of object from pinhole be x
6/24 = 10/x
6x = 240
x= 240/6
x = 40 cm
Calculate the current passing through a conductor of resistance 4ohms. If a potential difference of 15V its ends______
Explanation:
current = velocity/resistance
I = V/R
15/4
current = 3.75A
hope this helps...
what is the distance fallen for a freely falling ojvect 1 s after being dropped from a rest position
Answer:
111op
Explanation:
Answer:
11op
Explanation:good job and work hard
Determine the gradient and the co-ordinates of the x and y intercept of line whose equation is 2y + 3x = 1
Answer:
The x - intercept is 1/3
The y - intercept is 1/2
The gradient is -3/2
Explanation:
To find the x - intercept of the equation 2y + 3x = 1, we find the value of x when y = 0. So,
2y + 3x = 1
2(0) + 3x = 1
0 + 3x = 1
3x = 1
x = 1/3
So, the x - intercept is 1/3
To find the y - intercept of the equation 2y + 3x = 1, we find the value of y when x = 0. So,
2y + 3x = 1
2y + 3(0) = 1
2y + 0 = 1
2y = 1
y = 1/2
So, the y - intercept is 1/2
To find the gradient of the equation 2y + 3x = 1, we re-write it in gradient intercept form by making y subject of the formula.
So, 2y + 3x = 1
2y = -3x + 1
y = -3x/2 + 1/2
The coefficient of x which equals -3/2 is the gradient.
The gradient is -3/2
Which of these is an example of an elastic collision? A. The cue ball crashing into the eight balls on a pool table. B. Two cars colliding in an accident and moving together in the end. C. A kid landing a flip on a trampoline.
Answer:
The cue ball crashing into the eight balls on a pool table.
Explanation:
Elastic and inelastic collisions are two types of collisions.
For elastic collision, both the momentum and the kinetic energy before and after the collision remains conserved.
Out of the given options, the option that shows an example of an elastic collision is option A " The cue ball crashing into the eight balls on a pool table." All the eight balls after crashing moves with different velocity.
what is the scientific notation for 1,500,000
Answer:
[tex]1.5 * 10^6[/tex]
Explanation:
Given
Digit: 1,500,000
Required
Represent using scientific notation
We start by expressing the given digit as a product of 1.5 and a multiple of 10
[tex]Digit = 1.5 * 1,000,000[/tex]
1,000,000 can be represented as 10⁶
So; the digit becomes
[tex]Digit = 1.5 * 10^6[/tex]
Hence, the scientific notation of 1,500,000 is 1.5 * 10⁶
A bicycle has a momentum of 36 kg • m/s and a velocity of 4 m/s. What is the mass of the bicycle? 9 kg 32 kg 40 kg 144 kg
Answer:
9 kg
Explanation:
Momentum is mass times velocity.
p = mv
36 kgm/s = m (4 m/s)
m = 9 kg
The mass of the bicycle is 9 kg.
Momentum of the bicycle
The momentum of the bicycle is the product of mass and velocity of the bicycle.
P = mv
where;
P is momentumm is mass v is velocitym = P/v
m = 36/4
m = 9 kg
Thus, the mass of the bicycle is 9 kg.
Learn more about momentum here: https://brainly.com/question/7538238
a body weighs 100newtons when submerged in water. calculate the upthrust action on the body
Answer:
Upthrust = 20 N
Explanation:
The question says that "A body weighs 100N in air and 80N when submerged in water. Calculate the upthrust acting on the body ?"
Upthrust is defined as the force when a body is submerged in liquid, then liquid applies a force on it.
ATQ,
Weight of body in air is 100 N
Weight of body in water is 80 N
Upthrust is equal to the weight of body in air minus weight of body in water.
Upthrust = 100 N - 80 N
Upthrust = 20 N
So, 20 N of upthrust is acting on the body.
you walk 6 block east, 2 blocks north, 3 blocks west and then 2 blocks north. the total distance you travel is blocks
Answer:
The answerI travel 13 blocks16. Two of Jupiter's Galilean moons, lo and
Europe, make a complete revolution around it
over the periods T1=1.77 days and T2 = 3.55
days. Knowing that lo revolves around Jupiter
at a distance of 421600 km, determine the
linear velocity of Europe's motion in its orbit.
Answer:
The linear velocity of europe's motion in its orbit is 7875.58 km/hr.
Explanation:
Given that,
Time period of lo = 1.77 days
Time period of europa = 3.55 days
Distance of lo from jupiter = 421600 km
We know that,
Distance of europa from jupiter = 671000 km
We need to calculate the linear velocity of europe's motion in its orbit
Using formula of velocity
[tex]v=\dfrac{d}{t}[/tex]
Where, d = distance between europa and jupiter
t = time
Put the value into the formula
[tex]v=\dfrac{671000}{3.55\times24}[/tex]
[tex]v=7875.58\ km/hr[/tex]
Hence, The linear velocity of europe's motion in its orbit is 7875.58 km/hr.
An object weighs 980N on the earth’s surface (i) What is its mass? (ii) If the same object weighs 360N on another planet, find the force of gravity on that planet.
describe three way of nitrogen fixation in nature ?
Explanation:
nitrogen fixation is the process by which nitrogen gas form the atmosphere is converted into different compound that can be used by plants and animal. there are three major ways in which this happens: first, by lightning, second by industrial methods and finally by bacteria living in the soil.
A gauge is reading the pressure at the bottom of a river, at a depth of 6 m. Would the reading be greater or smaller than the reading at the bottom of a lake at the same depth? You must provide a clear explanation for full credit.
Answer:
The pressure at the bottom of the river is less than that at the bottom of the lake.
Explanation:
From Bernoulli's equation, the pressure difference is given by
ΔP = ρgΔh + ρ(v₂² - v₁²)/2 where ρ = density of water, g = acceleration due to gravity, Δh = depth, v₁ = velocity at top, v₂ = velocity at bottom
For the lake, v₁ = v₂, since the velocity at the top and bottom are the same. So,
ΔP₁ = ρgΔh + ρ(v₁² - v₁²)/2 = ρgΔh + 0 = ρgΔh
P₂ - P₁ = ρgΔh
P₂ = P₁ + ρgΔh
For the river, v₁ < v₂, since the velocity at the top of the river is greater than at the bottom.
So,
ΔP₂ = ρgΔh + ρ(v₂² - v₁²)/2.
Since v₁ < v₂, ρ(v₂² - v₁²)/2 will be negative,
So,
ΔP₂ = ρgΔh - ρ(v₂² - v₁²)/2.
Since ρ(v₂² - v₁²)/2 is negative, making ΔP less than that in the lake.
So, ΔP₂ = ΔP₁ - ρ(v₂² - v₁²)/2.
ΔP₂ = P₃ - P₁
P₃ - P₁ = P₂ - P₁ - ρ(v₂² - v₁²)/2.
P₃ = P₂ - ρ(v₂² - v₁²)/2.
where P₃ = pressure at bottom of the river and P₂ = pressure at bottom of the lake and P₁ = atmospheric pressure at top of river and lake respectively.
Since the factor ρ(v₂² - v₁²)/2 is removed from the pressure at the bottom of the lake, the pressure at the bottom of the river is therefore less than that at the bottom of the lake.
An object accelerates to a velocity of 230 m/s over a time of 2.5 s. The acceleration it experienced was 42 m/s2. What was its initial velocity?
Answer:
230 = x + 105
x= 125
Explanation:
v = v0 + at
SHOW ADEQUATE WORKINGS IN THIS SECTION
12. Wale and Lekan of 55kg and 60kg respectively ran a race of 200m.
i. Calculate their work done in KJ
ii. If wale finished the race in 25secs while Lekan finished in 30secs, calculate their
power and who is more powerful out of these two. ( g = 10m/secs)
13. A machine has a velocity ratio of 5 and is 800
/0 efficient. If the machine is carrying a load
of 200kg, what will be effort applied?
Please help me answer anyone that you understand
Answer:
12 i. The work done by Wale = 107.910 kJ
The work done by Lekan = 117.720 kJ
Total work done = 225.36 kJ
ii. Wale's power = 4.3164 kW
Lekan's power = 3.924 kW
Wale has more power and is more powerful than Lekan
13. 313.92 N
Explanation:
i. The work done, W = Force, F × Distance moved by the force, D
The given parameters are
The mass of Wale = 55 kg
The mass of Lekan = 60 kg
The acceleration due to gravity, g =9.81 m/s²
The motion force of Wale and Lekan are;
Motion force of Wale = 9.81 × 55 = 539.55 N
Motion force of Lekan = 9.81 × 60 = 588.6 N
The work done by Wale = 539.55 × 200 = 107910 J = 107.910 kJ
The work done by Lekan= 588.6 × 200 = 117720 J = 117.720 kJ
107910 + 117720 =225630 J = 225.36 kJ
ii. Power = Work done/time
Wale finished the race in 25 s, therefore, his power = 107910/25 = 4316.4 W
Lekan finished the race in 30 s, therefore, his power = 117720/30 = 3924 W
Wale has more power and is more powerful than Lekan
13. The velocity ratio = 5
V. R. = Distance moved by effort/(Distance moved by load)
Efficiency = 80%
Work done by effort = x
Work done by machine = Efficiency × Work done by effort = 0.8 × x
Distance moved by effort, E = V. R. × Distance moved by load, D = 5 × D
Work done by effort = Force × Distance moved = 200×9.81× E
Work done by effort = 1962×E = 1962×E = 1962×5×D
Work done by machine = 1962 × D, when D = 1, we have;
0.8 × 1962×1 = 1569.6 J
Work done by effort = Force × Distance moved
Work done by effort = Force × 5×D = Force × 5 (D = 1)
From the principle of conservation of energy, we have;
Energy is neither created nor destroyed
Therefore
Work done by effort = Force × 5 = 1569.6 J
Force = 1569.6 /5 = 313.92 N.
